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Knowledge Reasoning Method of Boolean Satisfiability (SAT)

a boolean satisfiability and knowledge reasoning technology, applied in knowledge based models, instruments, computing, etc., can solve the problems of solving algorithms that have been proposed and implemented, and none of them can reach a polynomial-time efficiency

Inactive Publication Date: 2014-09-25
HAN SHERWIN +1
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  • Application Information

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Benefits of technology

The present invention is a method and system for solving the Boolean SAT problem using a patented technology that combines knowledge learning and cognitive logic reasoning. The method and system employ a linear-time efficiency solution. The knowledge learning technology includes a pair of hierarchical mirrored languages that are used to convert SAT formula into a complement conjunction form and learn it as element-class relations among its classes of variables, literals, words, and clauses. The method and system use a patented deduction and reduction method to retrieve the element-class relations of the data between the mirrored languages. The method and system also recognize and delete data that are not satisfiable. The remaining knowledge domain is provided as a countable range of assignments.

Problems solved by technology

Numerous solution algorithms have been proposed and implemented, however, none of them is able to reach a polynomial-time efficiency.

Method used

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  • Knowledge Reasoning Method of Boolean Satisfiability (SAT)
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  • Knowledge Reasoning Method of Boolean Satisfiability (SAT)

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Embodiment Construction

[0017]Elimination of OR Operator Method

[0018]The present knowledge reasoning method applies a patented knowledge acquisition and retrieval method disclosed in the US patent “Knowledge Acquisition and Retrieval Apparatus and Method” (U.S. Pat. No. 6,611,841) by the same inventor Sherwin Han. Knowledge reasoning method converts the disjunction of the literals of the formula clauses to its semantic equivalent conjunction of literals, and eliminates OR operators. Each 3SAT formula contains m disjunctive clauses, and each disjunctive clause can be represented by a set of eight conjunctive clauses including one complement. For example, disjunctive clause (xxx2˜x3) can be presented by a set of eight conjunctive clauses {(x1x2x3), (x1x2˜x3), x1˜x2x3), (x1˜x2˜x3), (˜x1x2x3), (˜x1x2˜x3), (˜x1˜x2x3), (˜x1˜x2˜x3)} in which (˜x1˜x2x3) is a complement of (x1x2˜x3). Clause (x1x2˜x3) means that (˜x1˜x2x3) is not satisfiable, and the rest of conjunctive clauses are satisfiable. Elimination of OR ope...

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Abstract

Disclosed is a knowledge reasoning method for solving Boolean Satisfiability problems. This method is one of the applications of the method disclosed in the US patent “Knowledge Acquisition and Retrieval Apparatus and Method” (U.S. Pat. No. 6,611,841). Disclosed method applies learning function to access iterative set relations among variables, literals, words and clauses as knowledge; And applies deduction and reduction functions to retrieve relations as reasoning. The process is a knowledge learning (KL) and knowledge reasoning algorithm (KRA). KRA abandons the “OR” operation of Boolean logic and processes only set relations of the data. The novelty of the disclosed method is the reversibility between the deduction and reduction. That is, KRA of Boolean Satisfiability applies a pair of perceptual-conceptual languages to learn member-class relations and retrieve information through deductive and reductive reasoning.

Description

FIELD OF THE INVENTION[0001]The present invention relates generally to solving the problem of Boolean Satisfiability, and more particularly to a method that applies knowledge learning and reasoning technology to solve Boolean Satisfiability problems in linear time.BACKGROUND OF THE INVENTION[0002]Boolean Satisfiability (SAT) is a problem that has both academic and practical significance. In the industry domain the methodology of solution is used to prove the correctness of digital logic circuits and for many other purposes. Numerous solution algorithms have been proposed and implemented, however, none of them is able to reach a polynomial-time efficiency. The present invention provides such a polynomial, more accurately, linear-time efficiency methodology of solving Boolean satisfiability problems.SUMMARY OF THE INVENTION[0003]The present invention is a method of solving Boolean Satisfiability (SAT) problem that employs a patented knowledge learning (KL) and cognitive logic reasonin...

Claims

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Application Information

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Patent Type & Authority Applications(United States)
IPC IPC(8): G06N5/02
CPCG06N5/02G06N5/022G06N5/00
Inventor HAN, SHERWINZHOU, CUIFENG
Owner HAN SHERWIN
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